Evolution of isolated streamwise vortices in the late stages of boundary layer transition

Experiments were conducted with two, smooth hills, lying well within the boundary layer over a flat plate mounted in a wind tunnel. One hill was shallow, with peak height 1.5 mm and width 50 mm; the other, steep, 3 mm high and 30 mm wide. Since the hills occupied one-half of the tunnel span, streamwise vorticity formed near the hills' edge. At a freestream speed of 3.5 m/s, streaks formed with inflectional wall-normal and spanwise velocity profiles but without effecting transition. Transition, observed at 7.5 m/s, took different routes with the two hills. With the steep hill, streamwise velocity signals exhibited the passage of a wave packet which intensified before breakdown to turbulence. With the shallow hill there was a broad range of frequencies present immediately downstream of the hill. These fluctuations grew continuously and transition occurred within a shorter distance. Since the size of the streamwise vorticity generated at the hill edge is of the order of the hill height, the shallow hill generates vorticity closer to the wall and supports an earlier transition, whereas the steep hill creates a thicker vortex and associated streaks which exhibit oscillations due to their own instability as an additional precursor stage before transition.

Observation of reduced activation energy and the possible existence of decoupled pancake vortices in superconductor/ferromagnet bilayers

Investigations of different superconducting (S)/ferromagnetic (F) heterostructures grown by pulsed laser deposition reveal that the activation energy (U) for the vortex motion in a high T-c superconductor is reduced remarkably by the presence of F layers. The U exhibits a logarithmic dependence on the applied magnetic field in the S/F bilayers suggesting the existence of decoupled two-dimensional (2D) pancake vortices. This result is discussed in terms of the reduction in the effective S layer thickness and the weakening of the S coherence length due to the presence of F layers. In addition, the U and the superconducting T-c in YBa2Cu3O7-delta/La0.5Sr0.5CoO3 bilayers are observed to be much lower than in the YBa2Cu3O7-delta/La0.7Sr0.3MnO3 ones. This in turn suggests that the degree of spin polarization of the F layer might not play a crucial role for the suppression of superconductivity due to a spin polarized induced pair-breaking effect in S/F bilayers.

Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

Finite-temperature dynamics of vortices in Bose-Einstein condensates

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

Vortex reconnections between coreless vortices in binary condensates

Vortex reconnections plays an important role in the turbulent flows associated with the superfluids. To understand the dynamics, we examine the reconnections of vortex rings in the superfluids of dilute atomic gases confined in trapping potentials using Gross-Petaevskii equation. Further more we study the reconnection dynamics of coreless vortex rings, where one of the species can act as a tracer.

Chern-Simons vortices and holography

In this paper, based on the AdS(4)/CFT3 duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in (2 + 1) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that theU(1) current computed at the boundary of the AdS(4) could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in (2 + 1) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in (2 + 1) dimensions.

Electronic Properties of the Vortex State in Cuprate Superconductors

The superconducting state of the cuprates in the presence of a magnetic field has been investigated very actively in the past few years through measurements of electrical and thermal transport, ac conductivity, specific heat, and other quantities. The observed behavior is not well understood; it probes the nature of quasiparticies, vortices, and their interactions in a superconductor with nodes in the pair amplitude. We summarize here experimental results and our attempts to understand the phenomena.

Flow over a cylinder with a hinged-splitter plate

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a hinged-splitter plate in the wake of a circular cylinder. The splitter plate can rotate about the hinge at the base of the cylinder due to the unsteady fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted as in the rigid splitter plate case. In our study, we investigate this problem in the limit where the stiffness and internal damping associated with the hinge are negligible, and the mass ratio of the splitter plate is small. The experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re, Re>4000. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force, and has been observed previously for transversely oscillating cylinders with no restorin force. In the present case, the saturation tip amplitude level can be tip to 0.45D, where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter ratio (L/D) is crucial in determining the character and magnitude of the oscillations. For small splitter plate length (L/D <= 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The nondiinensional oscillation frequencies (fD/U) on the other hand are found to continuously vary with L/D from fD/U approximate to 0.2 at L/D = 1 to fD/U approximate to 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D >= 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D >= 5.0. In the present case of the hinged-splitter plate, the sudden transition seen as the splitter plate length (L/D) is increased from 3 to 4 may be attributed to the fact that the wake vortices are no longer able to synchronize with the plate motions for larger splitter plate lengths. Hence, as observed in other vortex-induced vibration problems, the oscillations becomeaperiodic and the amplitude reduces dramatically.

Fluid dynamics of the monsoon

The monsoonal regions of the world are characterized by a seasonal reversal in the direction of winds associated with the excursion of the equatorial trough (or the ITCZ) in response to the variation in the latitude of maximum insolation. This monsoonal circulation is a planetary scale phenomenon. However, the associated precipitation is critically dependent on the organization of the cumulus clouds (typically a few kilometers in horizontal extent) over the scale of synoptic vortices (typically a few hundred kilometers in horizontal extent). Thus modelling of the seasonal transitions and intraseasonal fluctuations requires an understanding of the fluid mechanics of these three scales of organizations and their interactions. The present paper is an attempt to outline the current state of understanding of these phenomena.

Flow Studies in Non Circular Tubes with Wall Injection

An analysis of inviscid incompressible flow in a tube of sinusoidally perturbed circular cross section with wall injection has been made. The velocity and pressure fields have been obtained. Measurements of axial velocity profiles and pressure distribution have been made in a simulated star shaped tube with wall injection. The static pressure at the star recess is found to be more than that at the star point, this feature being in conformity with the analytical result. Flow visualisation by photography of injected smoke seems to show simple diffusion rather than strong vortices in the recess.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

Large-scale structures in turbulent and reverse-transitional sink flow boundary layers

Aspects of large-scale organized structures in sink flow turbulent and reverse-transitional boundary layers are studied experimentally using hot-wire anemometry. Each of the present sink flow boundary layers is in a state of 'perfect equilibrium' or 'exact self-preservation' in the sense of Townsend (The Structure of Turbulent Shear Flow, 1st and 2nd edns, 1956, 1976, Cambridge University Press) and Rotta (Progr. Aeronaut. Sci., vol. 2, 1962, pp. 1-220) and conforms to the notion of 'pure wall-flow' (Coles, J. Aerosp. Sci., vol. 24, 1957, pp. 495-506), at least for the turbulent cases. It is found that the characteristic inclination angle of the structure undergoes a systematic decrease with the increase in strength of the streamwise favourable pressure gradient. Detectable wall-normal extent of the structure is found to be typically half of the boundary layer thickness. Streamwise extent of the structure shows marked increase as the favourable pressure gradient is made progressively severe. Proposals for the typical eddy forms in sink flow turbulent and reverse-transitional flows are presented, and the possibility of structural self-organization (i.e. individual hairpin vortices forming streamwise coherent hairpin packets) in these flows is also discussed. It is further indicated that these structural ideas may be used to explain, from a structural viewpoint, the phenomenon of soft relaminarization or reverse transition of turbulent boundary layers when subjected to strong streamwise favourable pressure gradients. Taylor's 'frozen turbulence' hypothesis is experimentally shown to be valid for flows in the present study even though large streamwise accelerations are involved, the flow being even reverse transitional in some cases. Possible conditions, which are required to be satisfied for the safe use of Taylor's hypothesis in pressure-gradient-driven flows, are also outlined. Measured convection velocities are found to be fairly close to the local mean velocities (typically 90% or more) suggesting that the structure gets convected downstream almost along with the mean flow.

A numerical study of the role of the vertical structure of vorticity during tropical cyclone genesis

An eight-level axisymmetric model with simple parameterizations for clouds and the atmospheric boundary layer was developed to examine the evolution of vortices that are precursors to tropical cyclones. The effect of vertical distributions of vorticity, especially that arising from a merger of mid-level vortices, was studied by us to provide support for a new vortex-merger theory of tropical cyclone genesis. The basic model was validated with the analytical results available for the spin-down of axisymmetric vortices. With the inclusion of the cloud and boundary layer parameterizations, the evolution of deep vortices into hurricanes and the subsequent decay are simulated quite well. The effects of several parameters such as the initial vortex strength, radius of maximum winds, sea-surface temperature and latitude (Coriolis parameter) on the evolution were examined. A new finding is the manner in which mid-level vortices of the same strength decay and how, on simulated merger of these mid-level vortices, the resulting vortex amplifies to hurricane strength in a realistic time frame. The importance of sea-surface temperature on the evolution of full vortices was studied and explained. Also it was found that the strength of the surface vortex determines the time taken by the deep vortex to amplify to hurricane strength.